The previous lecture in this series is here. The next lecture in this series is here.
We show the connection between compact subsets of a Hilbert space and closed, bounded subsets with equi-small tails (a result analogous to the Arzela-Ascoli Theorem). Then, we define finite-rank operators and compact operators.
These videos are of a lecture course by Casey Rodriguez at the Massachusetts Institute of Technology in 2021, and made available as part of its OpenCourseWare initiative.